Category Archives: Reflections

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In February, I was throwing together a geometry test for my 12-year-olds. I wanted a standard angle-chasing problem, but – and here’s the trick – I’m lazy. So I grabbed a Google image result, checked that I could do it in my head, and pasted it into the document.

But when I started writing up an answer key, I ran into a wall. Wait… how did I solve this last time? I trotted out all the standard techniques. They weren’t enough. A rung of the logical ladder seemed to have vanished overnight, and now I was stuck, grasping at air.

You know what’s often missing from math class? Yes, candy bars, but even more important than that: coherence.

Math class shouldn’t be a mishmash pile of facts, thrown together haphazardly, like an academic version of The White Album. It should be a perfectly interlocking tower of truths, climbing upwards with singular purpose—an academic Sgt. Pepper or Abbey Road.

A good class isn’t a greatest hits record. It’s a concept album.

In that spirit, I’ve been taking each topic in the secondary math curriculum—algebra, geometry, calculus, etc.—and trying to boil it down to its one-word essence. Here are the rules of the game:

You must choose a single word to complete the sentence, “[Branch of math] is the mathematics of _____.”

For example, you might say, “Topology is the mathematics of dinosaurs,” or “Category theory is the mathematics of abstraction,” or “Combinatorics is the mathematics of sadness.” (To be clear, only one of those is remotely accurate; you have my sympathy, combinatorists.)

In grad school, my wife took a class that assigned no homework. The topic was an advanced, hyper-specific area of research—the only plausible problems to give for homework had literally never been solved. Any answer to such a question would have constituted novel research, advancing the field and meriting a publication in a professional journal. The professor assigned no homework for the simple reason that there was no practical homework to assign.

This tickled me. I’d never thought of good questions like a fossil fuel. A nonrenewable resource. Built up over eons and consumed in minutes.

But the thought kept popping back up: Good questions are a resource. And in this new light, something started to make sense, an uncomfortable little fact that had nagged at me since my first year teaching. Continue reading →

This is my second century. I was 13 when it began—young enough to be almost fluent, but old enough that my technological skills retain a quaint 20th-century accent. (For example, I still use email.)

My parents’ generation, on the other hand, didn’t encounter the 21st century until they were full-grown adults. They’d settled into their habits when this digital tide began rising around them: Facebook, Twitter, viral videos, actual computer viruses, Android, Snapchat, gifs, Reddit…

And so was born that tragicomedy of 21st-century life: young people trying to explain technology to their parents. It’s frustrating both for the kids (“Why are you so incompetent?!”) and for the parents (“Why do I need this stupid device anyway?!”).

“This is so easy. Why can’t you do it?” vs. “This is so hard. What’s the point?” Now, why does that sound so familiar…?

Why 60 minutes per hour? Why 60 seconds per minute? It goes back to Babylon, with their base 60 number system—the same heritage that gives us 360 degrees in a circle. Now, that’s all well and good for Babylon 5 fans, but our society isn’t base-60. It’s base-10. Shouldn’t our system of measuring time reflect that?

So ring the bells, beat the drums, and summon the presidential candidates to “weigh in,” because I hereby give you… metric time.

Now, this represents a bit of a change. The new seconds are a bit shorter. The new minutes are a bit longer. And the new hours are quite different—nearly two and a half times as long.

Try asking adults about their math education: They refer to it like some sort of NCAA tournament. Everybody gets eliminated, and it’s only a question of how long you can stay in the game. “I couldn’t handle algebra” signifies a first-round knockout. “I stopped at multivariable calculus” means “Hey, I didn’t win, but I’m proud of making it to the final four.”

But there’s a new orthodoxy among teachers, an accepted wisdom which says, “Absolutely not.” Continue reading →